2 Answers
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I know a friend who had a similar problem. He had a 7/8 year old MacBook with 10.4 installed from factory that had two memory slots, but one of them had never been used up until very recently when he bought a second memory card. However, when he inserted the new memory card into the second slot, the computer would have a kernel panic more often than not. It turned out in the end that that specific slot had been built damaged, and since it had never been used, the time for warranty passed without any problem. He was told to, basically, buy a new computer because buying a new motherboard for such a relic was not worthwile. This seems like it is your problem...

Moral of the story: always test all your memory slots short after buying a new computer. It might save you from some serious trouble.

You've covered pretty much all the troubleshooting bases. If it's not a problem with the RAM itself, and it's not a problem with the firmware or software, it's almost certainly a hardware problem.

You could try running the Apple Hardware Test, but it's almost certainly a problem with the memory controller, which as far as I'm aware means a new logic board. Take it to an Apple Store or Authorized Service Provider.